This thesis investigates the trading on the London Stock Exchange, a multiple dealership market. It consists of four chapters. Chapter one motivates the study and summarises the major findings of the thesis. Chapter two examines the individual quoting behaviour of market makers. Quote revisions are often first made by one of the few price leaders in response to market information, and the rest follow suit. Price leaders tend to quote one side of the yellow strip to attract unbalanced orders; price followers often straddle the strip, which results in smaller but more balanced order flows. Moreover, the negative correlation between effective spreads and orders flows is detected in all but very small trades. The third chapter attempts to solve an apparent puzzle on the Exchange: market makers appear to charge different costs from different market participants. The chapter uses the theories of market microstructure to explain why the costs are different, and examines the extent to which the difference is related to the collusion of market makers or to the trading mechanisms. The evidence suggests the negotiation power of trading parties may play an important role in determining the costs of trades. The last chapter presents a new approach to estimate bid-ask spreads in multiple dealership markets. The traditional approach of estimating spreads is not applicable in those markets because observed prices cannot be ordered sequentially. An alternative method is proposed for which data sequentiality is not needed. The model is put into state space form to use the Kalman filter to estimate the fundamental price and the spread. The new method is implemented to the data of three liquid stocks on the Exchange.